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25 March, 09:38

A cylinder, with a piston pressing down with a constant pressure, is filled with 2.10 moles of a gas (n1), and its volume is 50.0 L (V1). If 0.300 mole of gas leak out, and the pressure and temperature remain the same, what is the final volume of the gas inside the cylinder?

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  1. 25 March, 09:50
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    42.86 L

    Explanation:

    The following data were obtained from the question:

    Initial mole (n1) = 2.10 moles

    Initial volume (V1) = 50.0 L

    Final mole (n2) = 2.10 - 0.3 = 1.8 mole

    Final volume (V2)

    From the ideal gas equation:

    PV = nRT

    Divide both side by P

    V = nRT/P

    Divide both side n

    V/n = RT/P

    Since the pressure (P) and temperature (T) are constant, therefore,

    V/n = constant

    V1/n1 = V2/n2

    V1 is the initial volume = 50L

    n1 is the initial mole = 2.1 moles

    V2 is final volume =.?

    n2 is the final mole = 1.8 mole

    V1/n1 = V2/n2

    50/2.1 = V2/1.8

    Cross multiply to express in linear form

    2.1 x V2 = 50 x 1.8

    Divide both side by 2.1

    V2 = (50 x 1.8) / 2.1

    V2 = 42.86 L

    Therefore, the final volume of the gas is 42.86 L
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